New reaching law for quasi-sliding mode control of discrete time systems

In this paper we consider the reaching law approach to the quasi-sliding mode control of discrete time systems. We analyze one of the most popular reaching laws which involves constant plus proportional decrease rate of the switching variable, and we propose a new version of this reaching law with the proportional part appropriately scaled. In our work the proportional part is scaled by a factor which depends on the current value of the switching variable. The reaching law introduced in this paper ensures quasi-sliding motion defined as remaining of the system representative point (state) in a band around the sliding hyperplane and crossing the hyperplane in each successive control period. The proposed reaching law guarantees faster convergence and offers better robustness with respect to external disturbances and modeling uncertainty than the previously presented reaching law characterized by the constant plus directly proportional decrease rate of the switching variable. Moreover, for a practically important class of time delay systems considered in the paper our reaching law ensures bounded control signal, which cannot be achieved with the reaching law proposed earlier.